Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds

TL;DR

This paper introduces Primal-Dual MCTS, a novel algorithm that uses sampled information relaxation bounds to focus on promising actions, enabling convergence to optimal decisions with shallower trees in complex decision problems.

Contribution

It proposes a new Monte Carlo Tree Search variant that incorporates upper bounds to ignore suboptimal branches, ensuring optimality despite partial tree expansion.

Findings

Primal-Dual MCTS produces deeper, more focused decision trees.

The method shows improved performance over standard MCTS.

It reduces sensitivity to large action spaces.

Abstract

Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the use of a heuristic, known as a default policy, to obtain Monte Carlo estimates of downstream values for states in a decision tree. This information is used to iteratively expand the tree towards regions of states and actions that an optimal policy might visit. However, to guarantee convergence to the optimal action, MCTS requires the entire tree to be expanded asymptotically. In this paper, we propose a new technique called Primal-Dual MCTS that utilizes sampled information relaxation upper bounds on potential actions, creating the possibility of "ignoring" parts of the tree that stem from highly suboptimal choices. This allows us to prove that despite converging to a partial decision tree in the limit, the recommended action from Primal-Dual MCTS is optimal. The new approach shows significant promise when used to optimize the behavior of a single driver navigating a graph while operating on a ride-sharing platform. Numerical experiments on a real dataset of 7,000 trips in New Jersey suggest that Primal-Dual MCTS improves upon standard MCTS by producing deeper decision trees and exhibits a reduced sensitivity to the size of the action space.